Question
Solve the inequation 2x – 5 ≤ 5x + 4 < 11, where x ∈ I. Also represent the solution set on the number line.
✓
Answer
$\begin{aligned} & 2 x-5 \leq 5 x+4<112 x-5 \leq 5 x+4 \\ & \Rightarrow 2 x-5-4 \leq 5 x \text { and } 5 x+4<11 \\ & \Rightarrow 2 x-9 \leq 5 x \text { and } 5 x<11-4 \\ & \text { and } 5 x<7 \\ & \Rightarrow 2 x-5 x \leq 9 \text { and } x<\frac{7}{5} \\ & \Rightarrow 3 x>-9 \text { and } x<1.4 \\ & \Rightarrow x>-3\end{aligned}$
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